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3.9 Connecting Variation, Slope and First Differences
1. Look at this graph of a relation.
3. A relation is represented by the equation
y = 3x – 5.
a) Is this relation a direct variation or a partial
variation?
b) Identify the initial value of y. ______________
c) Identify the constant of variation. __________
d) Make a table of values for x-values from 0 to 4.
x
y
0
1
2
3
4
e) Graph the relation.
a) Calculate the slope.
b) Determine the vertical intercept.
c) Write an equation for the relation of the form
y = mx + b.
y
7
6
5
4
3
2. Look at this graph of a relation.
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
a) Calculate the slope.
b) Determine the vertical intercept.
c) Write an equation for the relation of the form
y = mx + b.
x
1
2
3
4
5
6
7
8
9
4. The table represents a relation.
x
y
0
1
2
3
4
–1
3
7
11
15
a) Use a graph to represent the relation
b) Use words to represent the relation.
c) Identify the vertical intercept and the slope. Write an
equation to represent the relation.
5. A large cheese pizza costs $8.00, plus $0.50 for each topping.
a) Make a table to represent the relation.
b) Graph the relation.
c) Write an equation to represent the relation.
6. Represent this relation using words, with numbers,
and with an equation.
7. Write the equation of the horizontal
line passing through the point
.
8. What are the similarities and differences
between: linear relation, slope, constant
variation, rate of change, common first
differences?